Question

Let us consider a duopoly with homogeneous products, where two competing firms pick price (Bertrand duopoly). Suppose that Dogwood's marginal cost (MC) = $40 and Rose Petal's marginal cost (MC) - $35. Assume firms can set prices such as $29.99. Which of the following is true if both firms set a price as high as $60?

A. This is a Nash equilibrium because none of the firms will have an incentive to charge a different price as profits will be maximized. B. This is not a Nash equilibrium because both firms will have an incentive to charge a price slightly lower than $60.
C. This is not a Nash equilibrium because the revenue collected by each firm is less than its variable cost.
D. This is a Nash equilibrium because the revenue collected by each firm is more than its fixed cost.

Answer 1

The correct answer is B.

In a Bertrand duopoly with homogeneous products, the firms will not be at a Nash equilibrium when both set a price as high as $60. Each firm has an incentive to lower its price slightly to undercut the other, thus attracting the entire market.

Step-by-step explanation:

We are assuming a Bertrand duopoly situation where two firms produce homogeneous products and compete by setting prices. In such a scenario, both Dogwood and Rose Petal have set prices at $60 while having different marginal costs ($40 for Dogwood and $35 for Rose Petal).

Choice B is correct. This is not a Nash equilibrium because both firms have an incentive to slightly undercut the price in order to capture the entire market. If Dogwood or Rose Petal lowers their price even by a small amount, such as $59.99, they would attract all customers (since the products are homogeneous) and thereby increase their profit.

In a Bertrand duopoly, firms are incentivized to undercut each other until the price reaches the level of the marginal cost of the firm with the lowest marginal cost.

Choices A, C, and D are incorrect. A Nash equilibrium would occur only if lowering prices would not increase profits for either firm, which is not the case here. The revenue being more or less than respective variable or fixed costs is not what determines a Nash equilibrium in this context.

Therefore, unless collusion occurs or some form of price rigidity is present, it is unlikely for both firms to maintain a price of $60 and be at equilibrium.